Comparative study of model kinetic equations and the Boltzmann equation in the shock wave structure problem

In the current paper we compare numerical results obtained with the model kinetic equations and the Boltzmann transport equation. The classical problem of shock wave internal structure is solved with a deterministic solver implemented on a multi-GPU cluster. The Boltzmann collision integral is calculated using a conservative interpolation scheme along with special quadrature formulas, a correction procedure for distribution functions close to the Maxwellian distribution and an adaptive algorithm of node selection. Numerical simulations are performed for a single-species gas at the shock wave Mach numbers M = 1.5 and 8 and for a binary mixture at M = 1.5.